The input data into the RVM fitter was a set of PAs and associated values of longitude, \(\phi \) , taken from the set of pulsars presented in [1]}. The PAs were derived from Stokes Q and U, and were only determined when the linear polarization was more than \(5\sigma \)  significant. Error bars on the PAs were obtained from the value of the linear polarization compared to the noise using the procedure from [2]}. The peak of the profile was generally chosen as the zero point of longitude. RVM fitting was carried out using a least-squares procedure implemented in python. A total of 85 trials in \(\alpha \)  were used ranging from 5 to 175. In \(\beta \) , 40 trials were used, initially between \(\pm \) 20, a range which could be refined on subsequent runs. For each \(\alpha \) ,\(\beta \)  pair, the scipy routine least_squares was used to determine the values of \(\phi _0\)  and PA\(_0\)  which minimized \(\chi ^2\)  and the minimum \(\chi ^2\)  was recorded. We note that PAs can only lie between \(-90\)  and \(+90\)  and hence the phase-wraps need to be taken into account. In addition, radio emission can appear in two orthogonal modes, and these so-called orthogonal mode transitions must also be built into the fitting routine.
